1. Field of the Invention
The present invention relates generally to antennas.
2. Description of the Related Art
Metamaterials are structures engineered to have features of a size substantially less than that of an associated electromagnetic guided wavelength and configured to obtain negative permittivity, permeability and refractive index with that radiation.
In an electromagnetic wave, phase velocity is the velocity of the peaks of the wave traveling through a medium. In contrast, group velocity refers to a signal that is composed of electromagnetic waves within a frequency band and it is the velocity with which the entire group of frequencies travel, i.e. the signal energy flow. The group velocity cannot exceed the speed of light and the progression of an electromagnetic wave through a particular medium is dependent on the permittivity and permeability of the medium.
Permittivity relates to the medium's ability to transmit or “permit” an electric field. In particular, permittivity ∈ of a medium is defined as the ratio of the flux density produced by an electric field across that medium to the flux density produced by the same field in a vacuum. Permeability μ is the measure of the ability of a medium to support the formation of a magnetic field. If either but not both of the permittivity and permeability of a medium is negative, electromagnetic fields will not propagate but, rather, will decay exponentially into the medium.
If, however, the permittivity and permeability are both positive, the product ∈μ is positive and electromagnetic waves will propagate through the medium. In this case direction of the phase velocity vp is in the same direction as the energy flow Ef and this latter direction is defined by the cross product of the electric and magnetic fields E and H as shown in the graph 20 of FIG. 1. Such a medium is termed a right-handed (RH) medium. If the permittivity and permeability are both negative, the product ∈μ is again positive and electromagnetic waves will propagate through that medium. In this case, however, the direction of the phase velocity vp is opposite to the direction of the energy flow, i.e., the group velocity, as shown in the graph 21 of FIG. 1. Such a medium is termed a left-handed (LH) medium.
The refractive index n of a medium is defined as the phase velocity of an electromagnetic wave in vacuum divided by its velocity in the medium. Because the phase velocity direction is opposite the energy flow direction in a left-handed medium, this medium has a negative refractive index. As a consequence, a diverging lens of a right-handed material acts a converging lens when formed with a left-handed material and a converging lens of a right-handed material acts a diverging lens when formed with a left-handed material.
Dispersion is the phenomenon in which the phase and group velocities of an electromagnetic wave in a medium are a function of the frequency of the wave. A familiar result of dispersion is that of a rainbow in which dispersion causes white light to be spatially separated into light of different colors.
A compound right/left handed (CRLH) unit cell 22 of a transmission line is shown in FIG. 2A to comprise series arms on each side of a shunt arm wherein each of the series arms are formed with a series arrangement of an inductor Lr and a capacitor Cl and the shunt arm is formed with a parallel arrangement of an inductor Ll and a capacitor Cr.
At a resonant angular frequency ωres common to both the series and shunt arms, the series arms have a zero reactance and the shunt arm has an infinite reactance. Below ωres however, the unit cell 22 essentially reduces to the high-pass structure 24 of FIG. 2B that is formed by the left-handed components Cl and Ll of the unit cell 22. Above ωres, the unit cell 22 essentially reduces to the low-pass structure 26 of FIG. 2C that is formed by the right-handed components Cr and Lr of the unit cell.
A dispersion graph 25 in FIG. 2B plots angular frequency ω (radians per second) as a function of a propagation constant β (radians per the unit cell of the transmission line). A solid-line plot 26 in this graph shows the dispersion for frequencies less than ωres and shows that the phase velocity vp (ω/β) of the high-pass structure 24 is negative and rises to the resonant angular frequency ωres. The slope of a broken line from the origin of the graph 25 to a point on curve 26 represents the phase velocity at that point (frequency) on the plot 26 and the slope of a broken line tangent to the curve at that point represents the group velocity vg (δω/δβ).
In a similar graph 27 in FIG. 2C, a solid-line plot 28 shows the dispersion for frequencies greater than ωres and shows that the phase velocity vp of the low-pass structure 26 is positive and is in the same direction as group velocity i.e. both slopes are positive. Again, the slope of a broken line from the origin of the graph 27 represents the phase velocity at a particular point (frequency) on the curve 28 and the slope of a broken line tangent to the curve at that frequency represents the group velocity vg.
In the dispersion graph 25, the phase velocity is negative but the group velocity is positive. This indicates a non-evanescent backward wave in which permittivity and permeability are both negative so that we have the dispersion of an LH transmission line. In the dispersion graph 27, the phase velocity and group velocity are both positive. This indicates a forward wave in which permittivity and permeability are both positive so that we have the normal dispersion of an RH transmission line. Phase velocity at the resonant angular frequency ωres approaches infinity in the limit so that wavelength also approaches infinity.